Sándor Végh was born in 1912 in Kolozsvár, Transylvania, Kingdom of Hungary (since 1920 Cluj-Napoca, Romania). He began studying the piano at the age of six. He entered the Budapest Conservatory in 1924, taking violin studies with Jenő Hubay and composition with Zoltán Kodály. He began a career as a solo violinist and in 1927 played a Richard Strauss composition under the composer’s baton. He graduated from the Conservatory in 1930, having won the Hubay Prize and the Reményi Prize from the institution in 1927.
As his solo career was developing, he joined the Hungarian Trio with Ilonka Krauss and László Vencze. In 1934 he became one of the founding members of the Hungarian String Quartet. He was initially the first violin, but gave that position to Zoltán Székely and took second chair. He participated with the Hungarian String Quartet in the first Hungarian performance of Béla Bartók's String Quartet No. 5.
Végh left the Hungarian Quartet in 1940 to found his own quartet, the Végh Quartet. During the same season he became a professor at the Franz Liszt Academy of Music in Budapest. He and the quartet left Hungary in 1946. The quartet continued to give concerts until the mid-1970s; Végh also made solo appearances as a violinist. He took French citizenship in 1953.
In 1952 he met cellist Pablo Casals, who invited Végh to join him in giving summer classes in Zermatt, Switzerland (1953–62), and to appear annually in Casals' Prades Festival (1953–69). He found teaching rewarding, and thereafter taught at the Basel Conservatory (1953–63), in Freiburg (1954–62), Düsseldorf (1962–69) and at the Mozarteum in Salzburg (1971–97).
He founded the International Chamber Music Festival of Cervo in 1962 and often conducted there. He founded the Sándor Végh Chamber Orchestra and conducted it for a term lasting from 1968 to 1971, and conducted the Marlboro[disambiguation needed] Festival Orchestra (1974–77). In 1972, following an invitation to visit Cornwall from Hilary Tunstall-Behrens, he founded the International Musicians Seminar Prussia Cove http://www.i-m-s.org.uk/. In 1978 he became conductor of the Camerata Academica at the Mozarteum. With them he made a recording of Mozart’s divertimentos and serenades that won the Grand Prix du Disque in 1989.
He was awarded "Chevalier de la Légion d'honneur" in 1986, Doctor Honoris causa of Warwick and Exeter universities (1987), an honorary appointment as Commander of the Order of the British Empire (CBE) in 1988, and the Gold Medal of Salzburg in 1987.